anonymous
  • anonymous
In parallelogram PQRS, find the height h. Then calculate the area of PQRS.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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mathstudent55
  • mathstudent55
In a paralleogram, what do you know about opposite angles?
anonymous
  • anonymous
|dw:1437449376951:dw|
anonymous
  • anonymous
@mathstudent55 ∠R=45, ∠S=180-45=135, ∠P=45,and ∠Q=135.

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mathstudent55
  • mathstudent55
Correct. Opposite angles are congruent. |dw:1437450112404:dw|
mathstudent55
  • mathstudent55
That makes the small triangle on the left side a 45-45-90 triangle.
mathstudent55
  • mathstudent55
|dw:1437450166044:dw|
mathstudent55
  • mathstudent55
Since you have a 45-45-90 triangle, you can use the ratio of the length of the sides of a 45-45-90 triangle to find h.
mathstudent55
  • mathstudent55
Do you know the ratio of the sides of a 45-45-90 triangle?
anonymous
  • anonymous
1 to 1
anonymous
  • anonymous
\[\sqrt{2}\]
mathstudent55
  • mathstudent55
Yes, \(1 : 1 : \sqrt 2\) The hypotenuse is \(\sqrt 2\) times the length of either leg. The legs are congruent. The height of the parallelogram is the leg of the right triangle. What is the length of the leg?
anonymous
  • anonymous
8
mathstudent55
  • mathstudent55
Correct. Now you know the height of the parallelogram is 8. Do you know how to find the area of a parallelogram?
mathstudent55
  • mathstudent55
\(\Large A_{parallelogram} = bh\) where b = length of base, and h = height.
mathstudent55
  • mathstudent55
You were given a base of 20 cm, and you calculated a height of 8 cm.
anonymous
  • anonymous
A=bh. So A=20x8= 160cm^2
mathstudent55
  • mathstudent55
@SimiYami Do you understand how to find the area?
anonymous
  • anonymous
Yes, thank you for the help @mathstudent55. This is the exact answer in my book :D
mathstudent55
  • mathstudent55
You're welcome.

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